A plate is exactly one third of a brick in height (3.2 mm as in the diagram). In other words, 3 plates stack to match the height of a brick. This is useful to know if you're short on a certain size of brick, but have enough plates of the same shape and color to cover it in height.

While LEGO uses metric nowadays, you may be interested to know that the bricks they originally copied (and bought the patent for later on) were made in the UK and thus probably used imperial measurements (although dimensions are not specified in the original patent). You may want to search for UK patent 529580 or Kiddicraft to learn more about this. There may still be remnants of that English heritage buried deep in the LEGO legacy.

Also, when LEGO started, I'm not sure what their measurements or tolerance were at the time, but they probably weren't as strict as they are now, which may account for some oddities in the system. For example, the distance between studs has been measured as 7.986mm rather than an exact 8mm.

It looks like the number as the same as given in other sources, but there is disagreement about the height of a stud. I've seen the value 1.8mm (Robert), 1.7mm (Wikipedia) and 1.6mm (answers given here). Maybe the difference is because of the "LEGO" logo on top of a stud.

The stud height disagreement can be easily settled by examining a 1x1 headlight brick: The face with the headlight stud is inset by the 1.6mm base unit from the theoretical no-play boundary of the brick. If the stud was 1.6mm high, we should have no problem placing another brick in front of the headlight face. Even if the stud was 1.7mm high, the 0.1mm play would still allow this feat, albeit with a very tight fit.

Experience shows, howerver, that we can't fit another standard brick in front of a headlight brick, indicating that the headlight stud (which is hollow, so no logo involved here) has a height of more than 1.7mm, so you're safer to assume a height of 1.8mm.

(This stud height thing has been bothering me about Lego ever since the first day I tried to slot a plate between two rows of studs.)